Fragility to quantum fluctuations of classical Hamiltonian period doubling

We add quantum fluctuations to a classical Hamiltonian model with synchronized period doubling in the thermodynamic limit, replacing the $N$ classical interacting angular momenta with quantum spins of size $l$. The full permutation symmetry of the Hamiltonian allows a mapping to a bosonic model and the application of exact diagonalization for quite large system size. {In the thermodynamic limit $N\to\infty$ the model is described by a system of Gross-Pitaevski equations whose classical-chaos properties closely mirror the finite-$N$ quantum chaos.} For $N\to\infty$, and $l$ finite, Rabi oscillations mark the absence of persistent period doubling, which is recovered for $l\to\infty$ with Rabi-oscillation frequency tending exponentially to 0. For the chosen initial conditions, we can represent this model in terms of Pauli matrices and apply the discrete truncated Wigner approximation. For finite $l$ this approximation reproduces no Rabi oscillations but correctly predicts the absence of period doubling. Quantitative agreement is recovered in the classical $l\to\infty$ limit.